With　the　widespread　popularity　of　mobile　terminals　in　the　Internet　of　Things　(IoT),　the　demand　for　cross-domain　access　of　mobile　terminals　between　different　regions　has　also　increased　significantly.　The　nature　of　wireless　communication　media　makes　mobile　terminals　vulnerable　to　security　threats　in　cross-domain　access.　Identity　authentication　is　a　prerequisite　for　secure　data　transmission　in　the　cross-domain,　and　it　is　also　the　first　step　to　guarantee　the　credibility　of　data　sources.　Most　existing　authentication　schemes　are　based　on　bilinear　pairing　or　public-key　encryption　and　decryption　with　high　computation　overhead,　which　are　not　suitable　for　the　resource-limited　mobile　IoT　terminals.　Moreover,　these　schemes　have　some　security　drawbacks　and　cannot　meet　the　security　requirements　of　cross-domain　access.　In　this　article,　we　propose　a　lightweight　cross-domain　mutual　identity　authentication　(LCDMA)　for　the　mobile　IoT　environment.　LCDMA　uses　a　symmetric　polynomial　instead　of　high-complexity　bilinear　pairing　in　the　traditional　schemes.　We　theoretically　analyze　the　security　performance　under　the　random　oracle　model.　Our　results　show　that　LCDMA　not　only　resists　common　attacks　but　also　preserves　secure　traceability　while　guaranteeing　anonymity.　Performance　evaluation　further　demonstrates　that　our　scheme　has　better　performance　in　terms　of　computation　and　communication　overhead,　compared　with　other　existing　representative　schemes.